QCEVault

Rates of change and differential equations — Question 4

QCAA 2020, Paper 2 · 1 mark

Q4 · 2020 · Technology-activeSimple familiar1 mark

QUESTION 4

A particle is moving with simple harmonic motion described by the equation x=1.32cos⁡(πt2)x=1.32\cos\left(\frac{\pi t}{2}\right) where xx (m) is the displacement of the particle from a central position over time tt (s), t≥0t\ge0.
The maximum speed of the particle is
(A)
2.072.07 m s−1^{-1}
(B)
4.154.15 m s−1^{-1}
(C)
4.304.30 m s−1^{-1}
(D)
5.285.28 m s−1^{-1}
Question linkOriginal paper

Related questions

  1. Q13 · 2025 QCAA · Paper 1 · 5 marks
    The velocity (m s−1^{-1}) of a 3 kg object moving in a straight line is given by v=2cos⁡−1(x3),0≤x<3,v=2\cos^{-1}\left(\frac{x}{3}\right),\qquad0\le x<3, where xx is its position (m) from the origin.
    Rates of change and differential equations
  2. Q17 · 2025 QCAA · Paper 1 · 7 marks
    The radius of a cylinder decreases at a constant rate of 0.50.5 m s−1^{-1}, while maintaining a constant height of four metres. Given that the cylinder has an initial volume of 100π100\pi m3^3, determine the rate of change of the volume (m3^3 s−1^{-1}) of the cylinder after four seconds.
    Rates of change and differential equations
  3. Q18 · 2025 QCAA · Paper 1 · 6 marks
    An object is projected at an acute angle of θ\theta below the horizontal, with an initial speed of 30 m s−1^{-1} from a position 90 m above ground level. The object hits the ground 90 m horizontally from its projection point. Use vector calculus to determine θ\theta in its simplest form. Assume that the magnitude of mean acceleration due to gravity on Eart…
    Rates of change and differential equations
  4. Q6 · 2025 QCAA · Paper 2 · 1 mark
    Determine the gradient of the tangent to y2=4xy^2=4x when y=1y=1.
    Rates of change and differential equations